audras parents are both in their forties. the sum of their ages is ninety -two. the product of their ages is 2,107. how old is audras oldest parent?
Answer: Hello there!
Let's define x = age of parent 1, and y = age of parent 2, and suppose that y is the oldest one.
we know that:
x + y = 92
x*y = 2107
now we have a system of equations that we need to solve:
the first step is isolate one of the variables in one of the equation, let's isolate x in the first equation:
x = 92 - y
now we can replace it in the second equation and find the value of y.
x*y = 2107
y*(92 - y) = 2107
92y - y^2 = 2107
now we need to solve a cuadratic equation!
-y^2 + 92y - 2107 = 0
using the Bhaskara formula, we get:
[tex]y = \frac{-92 +/- \sqrt{92^{2} -4 *(-1)*(-2107) } }{-2} = \frac{-92 +/- \sqrt{36} }{-2} = \frac{-92 +/- 6}{-2}[/tex]
so we have two solutions:
y = (-92 + 6)/(-3) = 43
y = (-92 - 6)/(-2) = 49
because y is the oldest one, we need to take the biggest solution, this is y = 49.
so the oldest parent has 49 years.
if you want to find the age of the other parent, replace this in the first equation:
y + x = 92
49 + x = 92
x = 92 - 49 = 43
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Christopher just found beautiful yarn for 20% off at his favorite yarn store. He can make one scarf from 2/3 of a ball of yarn. If Christopher buys 12 balls of yarn, how many scarves can he make?
Answer:
16
Step-by-step explanation:
if 2/3 is used by one scarf, then we can divide 2/3 into 12
12/1 × 2/3
12/1 ×3/2= 36/2
36/2= 16
Christopher can create a total of 12 scarves with the 12 balls of yarn he buys, based on the ratio of 2/3 of a ball needed for one scarf.
Christopher can make scarves from yarn, where it takes 2/3 of a ball of yarn to make one scarf. If he buys 12 balls of yarn, we need to calculate the total number of scarves he can make.
Let's find out how many scarves he can create with 12 balls:
Firstly, determine how many scarf units are in one ball of yarn. Since it takes 2/3 of a ball to make a scarf, 1 ball equals 1.5 scarf units (since 1 / (2/3) = 1.5).Next, multiply the number of scarf units in one ball by the total number of balls. 1.5 scarf units per ball \\times 12 balls = 18 scarf units.Finally, since each scarf uses 2/3 of a ball, we divide the total number of scarf units by 1.5 to get the number of scarves. 18 scarf units / 1.5 = 12 scarves.Therefore, Christopher can make 12 scarves with 12 balls of yarn.
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How do you do 3.)and 3.a)
Figure PQRS is rotated by 180 degrees about the origin in the counterclockwise direction to obtain figure P′Q′R′S′:
Which statement best compares the lengths of the sides of the two figures?
Length of PQ = Length of P′Q′
Length of PQ = Length of R′S′
Length of RS = Length of P′Q′
Length of RS = Length of Q′R′
Answer:
A. Length of PQ = Length of P′Q′
Step-by-step explanation:
We are given,
Figure PQRS is rotated by 180° counter-clockwise about the origin to obtain P'Q'R'S'.
Since, we know that, 'Rotation' is a transformation that turns the figure around a fixed point to a certain degree.
We get that, rotation does not affect the length of the figure.
So, the length of PQ = length of P'Q' and length of RS = length of R'S'
Thus, according to the options, we get that option A i.e. Length of PQ = Length of P′Q′ is correct.
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A student is selling baked goods in the halls before school as a fundraiser. She sells cinnamon rolls, donuts, and croissants. Students purchase the goods according to the probability distribution:
X(Product): cinnamon roll, donut, croissant
P(x): 0.20, 0.55, 0.25
A): If a cinnamon roll yields $0.25 profit, a donut yields $0.20 profit, and a croissant yields a $0.30 profit, how much profit will be made on each customer?
B):If there are 50 customers, how much can you expect her to make?
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deena has a set of 4 coasters on her coffee table, and each coaster is shaped like a cylinder with a height of 0.5 inches and a radius of 2.5 inches. which is the total surface area of the 4 coasters?
Final answer:
The total surface area for the 4 cylindrical coasters, each with a height of 0.5 inches and a radius of 2.5 inches, is approximately 188.4956 square inches.
Explanation:
Deena has a set of 4 coasters, each shaped like a cylinder.
To calculate the surface area of one coaster, we need to find the area of the two circular bases and the area of the side that wraps around the cylinder (the lateral surface area).
The formula for the surface area of a cylinder is SA = 2πr(h+R), where r is the radius, h is the height, and R is the radius of the bases.
Given a height of 0.5 inches and a radius of 2.5 inches:
SA = 2π(2.5)(0.5+2.5)
SA = 2π(2.5)(3)
SA = 2π(7.5)
SA = 15π
The result is the surface area for one coaster. As we have 4 coasters, we multiply this result by 4:
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Select all that apply.
A point located at (5, -2) undergoes two transformations. Its image is located at (-5, 2). What were the transformations?
The point was reflected over the y-axis and translated up 4 units.
The point was translated right 10 units and reflected over the x-axis.
The point was translated left 10 units and up 4 units.
The point was reflected over the y-axis and translated down 4 units.
The point was reflected over the y -axis and translated up 4 units.
What is Transformation?A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.
We have,
A point located at (5, -2) undergoes two transformations.
Its image is located at (-5, 2).
The point was reflected over the y-axis and translated up 4 units, as shown by the coordinates becoming (-5, -2), respectively, when the point was reflected over the y-axis and (-5,2).
So, The point was reflected over the y -axis and translated up 4 units.
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For example, if you have a trapezoid with sides A and B, and the height is H, you can use these sides and the trigonometric principles to calculate the lengths of the bases. If side A or B is not perpendicular to the base, you would need to use the Pythagorean theorem. That formula is A^2+B^2=C^2, where C is the hypotenuse of the right triangle formed.
In case, the sides A and B are perpendicular to the base, the lengths of the bases would simply be side A + side B. This would give you the total length of the base of the trapezoid.
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